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A recent challenge in the modeling of particle flows is to build microstructure-informed drag models to overcome the average description of the fluid-particle force in the drag force correlations currently used in Euler-Lagrange and Euler-Euler models. To that end, we study through particle- resolved direct numerical simulations (PR-DNS) the flow past random assemblies of mono-dispersed spherical particles at three particle Reynolds numbers (10, 50, 100) and four solid volume fractions (0.10, 0.20, 0.30, 0.40). The present methodology is validated against theoretical and numerical results for the mean drag force in Stokes flows and finite Reynolds numbers flows. PR-DNS results are then used to characterize in details the statistics of the force distribution over the particle array, highlighting the substantial dispersion of the fluid force along the streamwise and transverse directions. The microstructure formed by the solid phase is described by means of a limited number of tensor quantities inspired from the fabric tensor used in granular media. Significant correlations are identified between the force experienced by a given particle immersed in a random array and a few key quantities that describe the anisotropy of its neighbourhood. A microstructure-based multi-linear model is proposed and validated against independent test cases. The model appears to perform best in the viscous and dense regimes. The addition of a stochastic contribution to the model allows to recover the correct level of force fluctuations at the cost of a lower correlation between the model and the data.

The propagation speeds of linear waves in gas-solid suspensions depend strongly on the solids volume fraction and the wave frequency. The latter is due to gas-solid momentum transfer and allows a simple test on filtered gas-solid momentum transfer models. Such models may predict linear wave propagation speeds different from those obtained with the nonfiltered model at wave frequencies higher than the filter frequency, but not at wave frequencies lower than the filter frequency. For the filtered drag, an effective drag coefficient approach is shown to alter the linear wave propagation speeds in the entire wave frequency range, independent of the applied effective drag coefficient. Furthermore, as the effective drag coefficient decreases, the high frequency linear wave propagation speeds are gradually introduced at lower wave frequencies. For the filtered momentum transfer due to the correlation between the solids volume fraction and the gas phase pressure gradient, the behavior of an apparent added mass closure model and an apparent history force closure model are investigated. An apparent added mass introduces the filter frequency linear wave propagation speeds to frequencies higher than the filter frequency. The linear wave propagation speeds for wave frequencies lower than the filter frequency are, however, not altered. Furthermore, an apparent added mass introduces no intrinsic wave frequency dependence in the linear wave propagation speeds, in agreement with its source term in the non-filtered model. Hence, the frequency dependence of the linear wave propagation speeds at frequencies lower than the filter frequency is still to be provided by a drag type term. As such, the behavior introduced by an apparent added mass is acceptable for filtered models. Also, to a certain extent, an apparent added mass can restore the linear wave propagation speed behavior at wave frequencies lower than the filter frequency altered by an effective drag coefficient approach. The reformulation of the apparent added mass in terms of an apparent distribution of the filtered gas phase pressure gradient over the phases and an apparent (effective) drag force is investigated. An apparent history force introduces intrinsic wave frequency dependence in the linear wave propagation speeds and alters the latter from the low wave frequencies on. As such, the behavior introduced by an apparent history force is unacceptable for filtered models, (C) 2006 Elsevier Ltd. All rights reserved.